Cytoskeletal networks play a key role in multiple mechanical and dynamical processes in cells. Recently, a continuum theory has been developed [1], allowing for the prediction of the material properties of highly crosslinked cytoskeletal networks from a phenomenological modelling of the microscopic interactions between the cytoskeleton filaments. We extend this theoretical framework to account for external forces, allowing us to explore how the properties of cytoskeletal networks are affected by the presence of various interfaces. This extended theory allows to study the interplay between cytoskeletal networks and the organelles that it interacts with, such as the centrosomes in spindles, vesicles embedded in intracellular actin networks, or even cortex-membrane interactions at the cell periphery.